dc.contributor.author | Bai, Ruobing | |
dc.contributor.author | Wu, Yifei | |
dc.contributor.author | Xue, Jun | |
dc.date.accessioned | 2021-03-05T15:20:08Z | |
dc.date.available | 2021-03-05T15:20:08Z | |
dc.date.created | 2020-09-29T14:19:10Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Journal of Differential Equations. 2020, 269 (9), 6422-6447. | en_US |
dc.identifier.issn | 0022-0396 | |
dc.identifier.uri | https://hdl.handle.net/11250/2731961 | |
dc.description.abstract | In this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \R\times \R. \end{align*} We prove that when $\sigma\ge 2$, the solution is global and scattering when the initial data is small in $H^s(\R)$, $\frac 12\leq s\leq1$. Moreover, we show that when $0<\sigma<2$, there exist a class of solitary wave solutions $\{\phi_c\}$ satisfying $$ \|\phi_c\|_{H^1(\R)}\to 0, $$ when $c$ tends to some endpoint, which is against the small data scattering statement. Therefore, in this model, the exponent $\sigma\ge2$ is optimal for small data scattering. We remark that this exponent is larger than the short range exponent and the Strauss exponent. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Elsevier | en_US |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no | * |
dc.title | Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | acceptedVersion | en_US |
dc.source.pagenumber | 6422-6447 | en_US |
dc.source.volume | 269 | en_US |
dc.source.journal | Journal of Differential Equations | en_US |
dc.source.issue | 9 | en_US |
dc.identifier.doi | https://doi.org/10.1016/j.jde.2020.05.001 | |
dc.identifier.cristin | 1834976 | |
dc.relation.project | Norges forskningsråd: 250070 | en_US |
dc.description.localcode | © 2020. This is the authors’ accepted and refereed manuscript to the article. Locked until 7/6-2022 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |